Gravitational force exerted by the sun on a

planet or by the earth on a satellite is an SOLUTION: important example of gravitational force. Write the radial and Newtons law of universal gravitation - two transverse equations of particles of mass M and m attract each other motion for the block. with equal and opposite force directed along the 5 line connecting the particles, 5 Integrate the radial equation A block B of mass m can slide freely on to find an expression for the Mm F =G 2 a frictionless arm OA which rotates in a radial velocity. r horizontal plane at a constant rate & . 0 Substitute known information G = constant of gravitation Knowing that B is released at a distance into m3 9 ft 4 r0 from O, express as a function of r the transverse equation to = 66.73 10 12 = 34 . 4 10 find an expression for the kg s 2 lb s 4 a) the component vr of the velocity of B force on the block. along OA, and For particle of mass m on the earths surface, b) the magnitude of the horizontal force MG m ft W =m 2 = mg g = 9.81 2 = 32.2 exerted on B by the arm OA. R s s2LDS LDSUnand Dipakai di lingkungan sendiri 9/23 Unand Dipakai di lingkungan sendiri 10/23

Results obtained for trajectories of satellites around earth may also be

applied to trajectories of planets around the sun.

Properties of planetary orbits around the sun were determined

astronomical observations by Johann Kepler (1571-1630) before 5 Newton had developed his fundamental theory. 1) Each planet describes an ellipse, with the sun located at one of its foci. 2) The radius vector drawn from the sun to a planet sweeps equal areas in equal times. 3) The squares of the periodic times of the planets are proportional to the cubes of the semimajor axes of their orbits.